دانلود کتاب Connections, Curvature, and Cohomology. Vol. 2: Lie Groups, Principal Bundles, and Characteristic Classes (Pure and Applied Mathematics Series; v. 47-II)

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Cover
Series
Title page
Date-line
Dedication
Contents
Preface
Introduction
Contents of Volumes I and III
Chapter 0 Algebraic and Analytic Preliminaries
1. Linear algebra
2. Homological algebra
3. Analysis and topology
4. Summary of volume I
Chapter I Lie Groups
1. Lie algebra of a Lie group
2. The exponential map
3. Representations
4. Abelian Lie groups
5. Integration on compact Lie groups
Problems
Chapter II Subgroups and Homogeneous Spaces
1. Lie subgroups
2. Linear groups
3. Homogeneous spaces
4. The bundle structure of a homogeneous space
5. Maximal tori
Problems
Chapter III Transformation Groups
1. Action of a Lie group
2. Orbits of an action
3. Vector fields
4. Differential forms
5. Invariant cross-sections
Problems
Chapter IV Invariant Cohomology
1. Group actions
2. Left invariant forms on a Lie group
3. Invariant cohomology of Lie groups
4. Cohomology of compact connected Lie groups
5. Homogeneous spaces
Problems
Chapter V Bundles with Structure Group
1. Principal bundles
2. Associated bundles
3. Bundles and homogeneous spaces
4. The Grassmannians
5. The Stiefel manifolds
6. The cohomology of the Stiefel manifolds and the classical groups
Problems
Chapter VI Principal Connections and the Weil Homomorphism
1. Vector fields
2. Differential forms
3. Principal connections
4. The covariant exterior derivative
5. Curvature
6. The Weil homomorphism
7. Special cases
8. Homogeneous spaces
Problems
Chapter VII Linear Connections
1. Bundle-valued differential forms
2. Examples
3. Linear connections
4. Curvature
5. Parallel translation
6. Horizontal subbundles
7. Riemannian connections
8. Sphere maps
Problems
Chapter VIII Characteristic Homomorphism for $\\Sigma$-bundles
1. $\\Sigma$-bundles
2. $\\Sigma$-connections
3. Invariant subbundles
4. Characteristic homomorphism
5. Examples
6. $\\Sigma$-bundies with compact carrier
7. Associated principal bundles
8. Characteristic homomorphism for associated vector bundles
Problems
Chapter IX Pontrjagin, Pfaffian, and Chern Classes
1. The modified characteristic homomorphism for real $\\Sigma$-bundles
2. Real bundles: Pontrjagin and trace classes
3. Pseudo-Riemannian bundles: Pontrjagin classes and Pfaffian class
4. Complex vector bundles
5. Chern classes
Problems
Chapter X The Gauss-Bonnet-Chern Theorem
Problems
Appendix A Characteristic Coefficients and the Pfaffian
1. Characteristic and trace coefficients
2. Inner product spaces
References
Bibliography
Chapters I-V
Chapters VI-X
Bibliography—Books
Notation Index
Index
Pure and Applied Mathematics Series